Digital Subscriber Line (xDSL) is a high-speed data transmission technology in which the data is transmitted on Unshielded Twist Pair (UTP) lines. Except for the xDSL based on the baseband transmission, such as ISDN DSL (IDSL), and Single-pair High-speed DSL (SHDSL), the xDSL based on the passband transmission uses Frequency Division Duplexing (FDD), so that the xDSL service and the Plain Old Telephone Service (POTS) may coexist on the same twisted pair. The xDSL service uses the high frequency band and the POTS uses the baseband below 4 KHz. The POTS signal and the xDSL signal are separated by a splitter. The xDSL based on the passband transmission uses the Discrete Multitone Modulation (DMT). The system, which provides the multiple xDSL access, is the Digital Subscriber Line Access Multiplexer (DSLAM). FIG. 1 shows the systemic model of the DSLAM.
As a transmission channel, the channel capacity of the phone twist pair must satisfy Shannon's channel capacity formula:
  C  =      B    ·                            log          2                ⁡                  (                      1            +                          S              N                                )                    .      
In Equation 1, C is the channel capacity, B is the signal bandwidth, S is the signal energy, and N is the noise energy. The channel capacity C may be improved by improving the signal bandwidth and the signal energy. The signal bandwidth B depends on the amplitude-frequency characteristic and the signal energy S is limited by the device, and the spectral compatibility. The signal bandwidth B and the signal energy S are both limited to a certain range. Accordingly, the transmission capacity of xDSL may not be further improved. The transmission capacity of the lines can be appropriately improved by reducing the noise energy N.
With the improvement of the frequency band employed by the xDSL technology, the crosstalk, such as the crosstalk in the high-frequency band, becomes prominent. Because the upstream and downstream channels of xDSL employ the FDMA, the Near-End crosstalk (NEXT) may hardly affect the capacity of the system. The Far-End crosstalk (FEXT) will affect the transmission capacity of the transmission line seriously. When a plurality of users based on the same cable requires activating the xDSL service, the FEXT may cause a low speed on some lines, an unstable performance or even an unactivable service. The outgoing line ratio of the DSLAM is low.
The vectored-DSL technology is proposed in the field. The vectored-DSL technology mainly utilizes the possibility of performing the tranceiving coordinately at the DSLAM end and uses the signal processing method to counteract interfere of the FEXT, so that no interfere of the FEXT exists in each signal and the transmission capacity is improved. FIG. 2 and FIG. 3 show that the DSLAM end sends signals simultaneously and the DSLAM end receives signals simultaneously, respectively.
The shared channel H shown in FIG. 2 and FIG. 3 may be represented with a matrix in the frequency domain as follows.
                              H          ⁡                      (            f            )                          =                              [                                          H                                  k                  ⁢                                                                          ⁢                  m                                            ⁡                              (                f                )                                      ]                                              k              =                              1                ⁢                                                                  ⁢                …                ⁢                                                                  ⁢                L                                      ,                          m              =                              1                ⁢                                                                  ⁢                …                ⁢                                                                  ⁢                L                                                                            =                              [                                                                                                      H                      11                                        ⁡                                          (                      f                      )                                                                                                                                  H                      12                                        ⁡                                          (                      f                      )                                                                                        …                                                                                            H                                              1                        ⁢                        L                                                              ⁡                                          (                      f                      )                                                                                                                                                              H                      21                                        ⁡                                          (                      f                      )                                                                                                                                  H                      22                                        ⁡                                          (                      f                      )                                                                                        …                                                                                            H                                              2                        ⁢                        L                                                              ⁡                                          (                      f                      )                                                                                                                    ⋮                                                  ⋮                                                  ⋱                                                  ⋮                                                                                                                        H                                              L                        ⁢                                                                                                  ⁢                        1                                                              ⁡                                          (                      f                      )                                                                                                                                  H                                              L                        ⁢                                                                                                  ⁢                        2                                                              ⁡                                          (                      f                      )                                                                                        …                                                                                            H                      LL                                        ⁡                                          (                      f                      )                                                                                            ]                                L            ×            L                              
In the matrix, Hkm(f) is an equation representing the transmission from line pair m to line pair k. When m=k, Hkm(f) represents a direct channel of line pair m, and when m≠k, Hkm(f) represents a crosstalk channel from line pair m to line pair k. The X(f) is an L×1 channel input vector, the Y(f) is an L×1 channel output vector, and N(f) is a noise vector. Therefore, the channel transmission equation is represented as follows.Y(f)=H(f)X(f)+N(f)
Because of using FDD technology in DSL, only the FEXT crosstalk is considered. The method for eliminating the crosstalk includes the QR decomposition method and the SVD decomposition method. In vector DSL, the downstream crosstalk is eliminated by the vector transmiter and the upstream crosstalk is eliminated by the vector receiver.
In QR decomposition method, Generalized Decision Feedback Equalization (GDFE) may be used to estimate the input vector X of the user. GDFE is similar to the DFE (a method for eliminating interferes between signals transmitted in a single channel) and can be applied to any channel in the form of y=Hx+n.
FIG. 4 is a diagram showing the downstream vector transmiter, and the detailed process of the downstream vector transmiter.
According to the QR decomposition method, HT matrix may also be represented as: HiT=Qi·Ri, and Ri is an upper triangular matrix, and Qi is a unitary matrix. For example, QiQi*=Qi*Qi=I, the superscript * represents the conjugation transpose transformation, and HiT is the transpose matrix of H. Hence, Hi=RiTQiT.
Assuming that xi=QiT*xi′ and xi′=Ri−Tdiag(RiT){tilde over (x)}i, and diag represents the diagonal matrix, then:
yi=Hixi+Ni=RiTQiTQiT*Ri−T diag(RiT){tilde over (x)}i+Ni. As for a channel without noise, the output is ŷ=diag(RiT){tilde over (x)}i, which is a diagonal matrix. Therefore, the crosstalk is eliminated.
For example, when L=4,
HiT=QiRi, and R may be represented as:
  R  =      [                                        R            11                                                R            12                                                R            13                                                R            14                                                0                                      R            22                                                R            23                                                R            24                                                0                          0                                      R            33                                                R            34                                                0                          0                          0                                      R            44                                ]  
Assuming that xi=QiT*xi′ and xi′=Ri−Tdiag(RiT){tilde over (x)}i, then
                              y          i                =                                            H              i                        ⁢                          x              i                                +                      N            i                                                  =                                            R              i              T                        ⁢                          Q              i              T                        ⁢                          Q              i                              T                *                                      ⁢                          R              i                              -                T                                      ⁢                          diag              ⁡                              (                                  R                  i                  T                                )                                      ⁢                                          x                ~                            i                                +                      N            i                                                  =                                            diag              ⁡                              (                                  R                  i                  T                                )                                      ⁢                                          x                ~                            i                                +                      N            i                                                  =                                            [                                                                                          R                      11                      T                                                                            0                                                        0                                                        0                                                                                        0                                                                              R                      22                      T                                                                            0                                                        0                                                                                        0                                                        0                                                                              R                      33                      T                                                                            0                                                                                        0                                                        0                                                        0                                                                              R                      44                      T                                                                                  ]                        ·                                          x                ~                            i                                +                      N            i                                                  =                              [                                                                                                      R                      11                      T                                        ⁢                                                                  x                        ~                                            1                                                                                        0                                                  0                                                  0                                                                              0                                                                                            R                      22                      T                                        ⁢                                                                  x                        ~                                            2                                                                                        0                                                  0                                                                              0                                                  0                                                                                            R                      33                      T                                        ⁢                                                                  x                        ~                                            3                                                                                        0                                                                              0                                                  0                                                  0                                                                                            R                      44                      T                                        ⁢                                                                  x                        ~                                            4                                                                                            ]                    +                      N            i                              
The outputs for four users are R11T{tilde over (x)}1, R22Tx2, R33Tx3, R44T{tilde over (x)}4, respectively. Therefore, the crosstalk is eliminated.
FIG. 5 is a diagram showing the upstream vector receiver.
According to the QR decomposition method, Hi matrix may also be represented as: Hi=Qi·Ri, and Ri is an upper triangular matrix, and Qi is a unitary matrix. For example, QiQi*=Qi*Qi=I. The superscript * represents the conjugation transpose transformation.
The upstream receiving vector is:Yi=Hixi+Ni 
Both sides of the above equation are multiplied by Qi*, thenŶi=Q*(Hixi+Ni)Ŷi=Qi*•Qi•Rixi+Qi*•Ni=Rixi+Qi*•Ni.
As shown in the above equation, when a channel is a channel without noise, the output is Ŷi=Rixi, 1≦i≦L. Ri is an upper triangular matrix.
The output value may be estimated by GDFE. As can be seen, the Lth output has a value without the crosstalk and the Lth output value may be obtained with a simple decoder. As for the (L−1)th output, the crosstalk on the (L−1)th line from the Lth line is eliminated by subtracting the Lth estimated result from the (L−1)th output. Through a simple estimation, the (L−1)th output value may be obtained. The first output value may be obtained by subtracting the previous estimated value one by one. Therefore, the crosstalk between lines is eliminated.
For example, when L=4,
Hi=QiRi, and Ri may be represented as:
      R    i    =      [                                        R            11                                                R            12                                                R            13                                                R            14                                                0                                      R            22                                                R            23                                                R            24                                                0                          0                                      R            33                                                R            34                                                0                          0                          0                                      R            44                                ]  
As for Yi=Hixi+Ni, both sides of the equation are multiplied by Qi*, then
                                          Y            ^                    i                =                                                            Q                i                *                            ·                              Q                i                *                            ·                              R                i                                      ⁢                          x              i                                +                                    Q              i              *                        ·                          N              i                                                              =                                            R              i                        ⁢                          x              i                                +                                    Q              i              *                        ·                          N              i                                                                        =                                                    [                                                                                                    R                        11                                                                                                            R                        12                                                                                                            R                        13                                                                                                            R                        14                                                                                                                        0                                                                                      R                        22                                                                                                            R                        23                                                                                                            R                        24                                                                                                                        0                                                              0                                                                                      R                        33                                                                                                            R                        34                                                                                                                        0                                                              0                                                              0                                                                                      R                        44                                                                                            ]                            ·                              x                i                                      +                                          Q                i                *                            ⁢                              N                i                                                    ;            as for a channel without noise,
                                          Y            ^                    i                =                              [                                                                                R                    11                                                                                        R                    12                                                                                        R                    13                                                                                        R                    14                                                                                                0                                                                      R                    22                                                                                        R                    23                                                                                        R                    24                                                                                                0                                                  0                                                                      R                    33                                                                                        R                    34                                                                                                0                                                  0                                                  0                                                                      R                    44                                                                        ]                    ·                      [                                                                                x                    1                                                                                                                    x                    2                                                                                                                    x                    3                                                                                                                    x                    4                                                                        ]                                                  =                  [                                                                                                                R                      11                                        ⁢                                          x                      1                                                        +                                                            R                      12                                        ⁢                                          x                      2                                                        +                                                            R                      12                                        ⁢                                          x                      3                                                        +                                                            R                      14                                        ⁢                                          x                      4                                                                                                                                                                                      R                      22                                        ⁢                                          x                      2                                                        +                                                            R                      23                                        ⁢                                          x                      3                                                        +                                                            R                      24                                        ⁢                                          x                      4                                                                                                                                                                                      R                      33                                        ⁢                                          x                      3                                                        +                                                            R                      34                                        ⁢                                          x                      4                                                                                                                                                                R                    44                                    ⁢                                      x                    4                                                                                ]                    
As can be seen, the fourth output has a value without the crosstalk, and the fourth user output value may be estimated through a simple decoder. The crosstalk on the third user from the fourth user is eliminated by subtracting the fourth estimated result from the third output. Through a simple estimation, the third user output value is obtained. The first user output value may be obtained by subtracting the previous estimated value one by one. Therefore, the crosstalk is eliminated.
The user channel information may be used for eliminating the crosstalk. However, when a user logs on, the user may cause the crosstalk on other user channel. Because the crosstalk cancellation device (or, the precoder) is calculated from the user channel information obtained by matrix H before the user logs on, the balance is broken and the crosstalk eliminating capacity is lowered.